Reparameterization-invariant reduction in the Hamiltonian description of arelativistic string

We study the time-reparameterization-invariant dynamics of an open relativi stic string using the generalized Dirac-Hamilton theory and resolving the c onstraints of the first kind. The reparameterization-invariant evolution va riable is the time coordinate of the string center of mass. Using a transfo rmation that preserves the diffeomorphism group of the generalized Hamilton ian and the Poincare covariance of the local constraints, we segregate the center-of-mass coordinates from the local degrees of freedom of the string. We identify the time coordinate of the string center of mass and the prope r time measured in the string frame of reference using the Levi-Civita-Shan mugadhasan canonical transformation, which transforms the global constraint (the mass shell) in the new momentum such that the Hamiltonian reduction d oes not require the corresponding gauge condition. Resolving the local cons traints, we obtain an equivalent reduced system whose Hamiltonian describes the evolution w.r.t. the proper time of the string center of mass. The Roh rlich quantum relativistic string theory, which includes the Virasoro opera tors L-n only with n > 0, is used to quantize this system. In our approach, the standard problems that appear in the, traditional quantization scheme, including the space-time dimension D = 26 and the tachyon emergence, arise only in the case of a massless string, M-2 = 0.